Quantifying intracortical bone microstructure: a critical appraisal of 2D and 3D approaches for assessing vascular canals and osteocyte lacunae

Describing and quantifying vascular canal orientation and volume of osteocyte lacunae in bone is important in studies of bone growth, mechanics, health and disease. It is also an important element in analysing fossil bone in palaeohistology, key to understanding the growth, life and death of extinct animals. Often, bone microstructure is studied using two-dimensional (2D) sections, and three-dimensional (3D) shape and orientation of structures are estimated by modelling the structures using idealised geometries based on information from their cross sections. However, these methods rely on structures meeting strict geometric assumptions. Recently, 3D methods have been proposed which could provide a more accurate and robust approach to bone histology, but these have not been tested in direct comparison with their 2D counterparts in terms of accuracy and sensitivity to deviations from model assumptions. We compared 2D and 3D methodologies for estimating key microstructural traits using a combination of experimental and idealised test data sets. We generated populations of cylinders (canals) and ellipsoids (osteocyte lacunae), varying the cross-sectional aspect ratios of cylinders and orientation of ellipsoids to test sensitivity to deviations from cylindricality and longitudinal orientation, respectively. Using published methods, based on 2D sections and 3D data sets, we estimated cylinder orientation and ellipsoid volume. We applied the same methods to six CT data sets of duck cortical bone, using the full volumes for 3D measurements and single CT slices to represent 2D sections. Using in silico test data sets that did deviate from ideal cylinders and ellipsoids resulted in inaccurate estimates of cylinder or canal orientation, and reduced accuracy in estimates of ellipsoid and lacunar volume. These results highlight the importance of using appropriate 3D imaging and quantitative methods for quantifying volume and orientation of 3D structures and offer approaches to significantly enhance our understanding of bone physiology based on accurate measures for bone microstructures.